Господин Экзамен
Другие калькуляторы
-
Как пользоваться?
- x^3+9*x*y-9*y^2+y^2-9*x^2 если y=3
- cos(x)^2-3*sin(x)*cos(x)+2*sin(x)^2 если x=-4
- 302*n-n если n=1/4
- cos(4*a) если a=-1
- Разложить многочлен на множители:
- z*d-18*z^n+16*d-288*n
- 64-125*y^3
- x^2-7+10
- 0.64*m^2-225
- Общий знаменатель:
- 3*c+5*d/(35*c*d)+c-3*d/(21*c*d)
- -300*pi/((1+10000/(pi*x+12)^6)*(pi*x+12)^4)
- (1/(m-n)*(n-k))-(1/(n-k)*(m-k))-(1/(k-m)*(n-m))
- (x+9)/x^2+18*x+81/x-9
- Умножение столбиком:
- 96*18
- 968*54
- 493*804
- 47*696
- Деление столбиком:
- 48048/6
- 3025/5
- 1860/6
- 2051/6
- Раскрыть скобки в:
- (y-9)^2-3*y*(y+1)
- x3*y3*x4*(-3)*y2
- 5*x^4*y*(-3)*x^2*y^3
- (c-9)*(c-3)-6*c*(3*c-2)
- Разложение числа на простые множители:
- 63973
- 7220
- 2770
- 2475
- График функции y =:
- -1
- Производная:
- -1
- Интеграл d{x}:
-
-1
-
Идентичные выражения
- cos(четыре *a) если a=- один
- косинус от (4 умножить на a) если a равно минус 1
- косинус от (четыре умножить на a) если a равно минус один
- cos(4a) если a=-1
- cos4a если a=-1
- cos(4*a) при a=-1
-
Похожие выражения
- tan(a)*sin(2*a)*cos(4*a) если a=1/3
- cos(4*a) если a=+1
- (1+cos(2*a))*(1+cos(4*a)) если a=-1/3
cos(4*a) если a=-1
Решение
Подстановка условия
[src]
cos(4*a) при a = -1
подставляем
cos(4*a)
$$\cos{\left(4 a \right)}$$
cos(4*a)
$$\cos{\left(4 a \right)}$$
переменные
a = -1
$$a = -1$$
cos(4*(-1))
$$\cos{\left(4 (-1) \right)}$$
cos(4)
$$\cos{\left(4 \right)}$$
cos(4)
Степени
[src]
-4*I*a 4*I*a e e ------- + ------ 2 2
$$\frac{e^{4 i a}}{2} + \frac{e^{- 4 i a}}{2}$$
exp(-4*i*a)/2 + exp(4*i*a)/2
Тригонометрическая часть
[src]
1 -------- sec(4*a)
$$\frac{1}{\sec{\left(4 a \right)}}$$
/pi \ sin|-- + 4*a| \2 /
$$\sin{\left(4 a + \frac{\pi}{2} \right)}$$
1 ------------- /pi \ csc|-- - 4*a| \2 /
$$\frac{1}{\csc{\left(- 4 a + \frac{\pi}{2} \right)}}$$
2
1 - tan (2*a)
-------------
2
sec (2*a)
$$\frac{- \tan^{2}{\left(2 a \right)} + 1}{\sec^{2}{\left(2 a \right)}}$$
2
-1 + cot (2*a)
--------------
2
1 + cot (2*a)
$$\frac{\cot^{2}{\left(2 a \right)} - 1}{\cot^{2}{\left(2 a \right)} + 1}$$
2 / 2 \ sin (2*a)*\-1 + cot (2*a)/
$$\left(\cot^{2}{\left(2 a \right)} - 1\right) \sin^{2}{\left(2 a \right)}$$
2
1 - tan (2*a)
-------------
2
1 + tan (2*a)
$$\frac{- \tan^{2}{\left(2 a \right)} + 1}{\tan^{2}{\left(2 a \right)} + 1}$$
2 / 2 \ cos (2*a)*\1 - tan (2*a)/
$$\left(- \tan^{2}{\left(2 a \right)} + 1\right) \cos^{2}{\left(2 a \right)}$$
1 2 cos(4*a) - - + cos (2*a) + -------- 2 2
$$\cos^{2}{\left(2 a \right)} + \frac{\cos{\left(4 a \right)}}{2} - \frac{1}{2}$$
1
1 - ---------
2
cot (2*a)
-------------
1
1 + ---------
2
cot (2*a)
$$\frac{1 - \frac{1}{\cot^{2}{\left(2 a \right)}}}{1 + \frac{1}{\cot^{2}{\left(2 a \right)}}}$$
/ pi\
2*tan|2*a + --|
\ 4 /
------------------
2/ pi\
1 + tan |2*a + --|
\ 4 /
$$\frac{2 \tan{\left(2 a + \frac{\pi}{4} \right)}}{\tan^{2}{\left(2 a + \frac{\pi}{4} \right)} + 1}$$
/ 4 \
2 | 4*sin (2*a)|
cos (2*a)*|1 - -----------|
| 2 |
\ sin (4*a) /
$$\left(- \frac{4 \sin^{4}{\left(2 a \right)}}{\sin^{2}{\left(4 a \right)}} + 1\right) \cos^{2}{\left(2 a \right)}$$
2
sec (2*a)
1 - --------------
2/ pi\
sec |2*a - --|
\ 2 /
------------------
2
sec (2*a)
$$\frac{- \frac{\sec^{2}{\left(2 a \right)}}{\sec^{2}{\left(2 a - \frac{\pi}{2} \right)}} + 1}{\sec^{2}{\left(2 a \right)}}$$
/ 2/ pi\\
| cos |2*a - --||
2 | \ 2 /|
cos (2*a)*|1 - --------------|
| 2 |
\ cos (2*a) /
$$\left(1 - \frac{\cos^{2}{\left(2 a - \frac{\pi}{2} \right)}}{\cos^{2}{\left(2 a \right)}}\right) \cos^{2}{\left(2 a \right)}$$
2 / 2 \ 4 / 2 \ \1 - tan (a)/ *cos (a)*\1 - tan (2*a)/
$$\left(- \tan^{2}{\left(a \right)} + 1\right)^{2} \cdot \left(- \tan^{2}{\left(2 a \right)} + 1\right) \cos^{4}{\left(a \right)}$$
/ 4 \
2/pi \ | 4*sin (2*a)|
sin |-- + 2*a|*|1 - -----------|
\2 / | 2 |
\ sin (4*a) /
$$\left(- \frac{4 \sin^{4}{\left(2 a \right)}}{\sin^{2}{\left(4 a \right)}} + 1\right) \sin^{2}{\left(2 a + \frac{\pi}{2} \right)}$$
2 / 2 2 \ 2 2 \cos (a) - sin (a)/ - 4*cos (a)*sin (a)
$$- 4 \sin^{2}{\left(a \right)} \cos^{2}{\left(a \right)} + \left(- \sin^{2}{\left(a \right)} + \cos^{2}{\left(a \right)}\right)^{2}$$
/ /pi \ | 0 for |-- + 4*a| mod pi = 0 < \2 / | \cos(4*a) otherwise
$$\begin{cases} 0 & \text{for}\: \left(4 a + \frac{\pi}{2}\right) \bmod \pi = 0 \\\cos{\left(4 a \right)} & \text{otherwise} \end{cases}$$
/ 4 \
| 4*sin (2*a)|
|1 - -----------|*(1 + cos(4*a))
| 2 |
\ sin (4*a) /
--------------------------------
2
$$\frac{\left(- \frac{4 \sin^{4}{\left(2 a \right)}}{\sin^{2}{\left(4 a \right)}} + 1\right) \left(\cos{\left(4 a \right)} + 1\right)}{2}$$
2/pi \
csc |-- - 2*a|
\2 /
1 - --------------
2
csc (2*a)
------------------
2/pi \
csc |-- - 2*a|
\2 /
$$\frac{1 - \frac{\csc^{2}{\left(- 2 a + \frac{\pi}{2} \right)}}{\csc^{2}{\left(2 a \right)}}}{\csc^{2}{\left(- 2 a + \frac{\pi}{2} \right)}}$$
4
4*sin (2*a)
1 - -----------
2
sin (4*a)
---------------
4
4*sin (2*a)
1 + -----------
2
sin (4*a)
$$\frac{- \frac{4 \sin^{4}{\left(2 a \right)}}{\sin^{2}{\left(4 a \right)}} + 1}{\frac{4 \sin^{4}{\left(2 a \right)}}{\sin^{2}{\left(4 a \right)}} + 1}$$
/ 1 for 2*a mod pi = 0 | | 2 <-1 + cot (2*a) |-------------- otherwise | 2 \1 + cot (2*a)
$$\begin{cases} 1 & \text{for}\: 2 a \bmod \pi = 0 \\\frac{\cot^{2}{\left(2 a \right)} - 1}{\cot^{2}{\left(2 a \right)} + 1} & \text{otherwise} \end{cases}$$
/ 1 for 2*a mod pi = 0 | < 2 / 2 \ |sin (2*a)*\-1 + cot (2*a)/ otherwise \
$$\begin{cases} 1 & \text{for}\: 2 a \bmod \pi = 0 \\\left(\cot^{2}{\left(2 a \right)} - 1\right) \sin^{2}{\left(2 a \right)} & \text{otherwise} \end{cases}$$
2
/ 2 \ / 2 \
\1 - tan (a)/ *\1 - tan (2*a)/
------------------------------
2
/ 2 \
\1 + tan (a)/
$$\frac{\left(- \tan^{2}{\left(a \right)} + 1\right)^{2} \cdot \left(- \tan^{2}{\left(2 a \right)} + 1\right)}{\left(\tan^{2}{\left(a \right)} + 1\right)^{2}}$$
/ 1 for 2*a mod pi = 0 | | 1 |-1 + --------- < 2 | tan (2*a) |-------------- otherwise | 2 \ csc (2*a)
$$\begin{cases} 1 & \text{for}\: 2 a \bmod \pi = 0 \\\frac{-1 + \frac{1}{\tan^{2}{\left(2 a \right)}}}{\csc^{2}{\left(2 a \right)}} & \text{otherwise} \end{cases}$$
/ 1 for 2*a mod pi = 0 | | 2 / 1 \
$$\begin{cases} 1 & \text{for}\: 2 a \bmod \pi = 0 \\\left(-1 + \frac{1}{\tan^{2}{\left(2 a \right)}}\right) \sin^{2}{\left(2 a \right)} & \text{otherwise} \end{cases}$$
/ 1 for 2*a mod pi = 0 | | 1 |-1 + --------- | 2 < tan (2*a) |-------------- otherwise | 1 |1 + --------- | 2 \ tan (2*a)
$$\begin{cases} 1 & \text{for}\: 2 a \bmod \pi = 0 \\\frac{-1 + \frac{1}{\tan^{2}{\left(2 a \right)}}}{1 + \frac{1}{\tan^{2}{\left(2 a \right)}}} & \text{otherwise} \end{cases}$$
2/ pi\
cos |2*a - --|
\ 2 /
1 - --------------
2
cos (2*a)
------------------
2/ pi\
cos |2*a - --|
\ 2 /
1 + --------------
2
cos (2*a)
$$\frac{1 - \frac{\cos^{2}{\left(2 a - \frac{\pi}{2} \right)}}{\cos^{2}{\left(2 a \right)}}}{1 + \frac{\cos^{2}{\left(2 a - \frac{\pi}{2} \right)}}{\cos^{2}{\left(2 a \right)}}}$$
2
sec (2*a)
1 - --------------
2/ pi\
sec |2*a - --|
\ 2 /
------------------
2
sec (2*a)
1 + --------------
2/ pi\
sec |2*a - --|
\ 2 /
$$\frac{- \frac{\sec^{2}{\left(2 a \right)}}{\sec^{2}{\left(2 a - \frac{\pi}{2} \right)}} + 1}{\frac{\sec^{2}{\left(2 a \right)}}{\sec^{2}{\left(2 a - \frac{\pi}{2} \right)}} + 1}$$
// 1 for a mod pi = 0\
/ 2 \ || |
\1 - tan (2*a)/*|<1 + cos(4*a) |
||------------ otherwise |
\\ 2 /
$$\left(- \tan^{2}{\left(2 a \right)} + 1\right) \left(\begin{cases} 1 & \text{for}\: a \bmod \pi = 0 \\\frac{\cos{\left(4 a \right)} + 1}{2} & \text{otherwise} \end{cases}\right)$$
2/pi \
csc |-- - 2*a|
\2 /
1 - --------------
2
csc (2*a)
------------------
2/pi \
csc |-- - 2*a|
\2 /
1 + --------------
2
csc (2*a)
$$\frac{1 - \frac{\csc^{2}{\left(- 2 a + \frac{\pi}{2} \right)}}{\csc^{2}{\left(2 a \right)}}}{1 + \frac{\csc^{2}{\left(- 2 a + \frac{\pi}{2} \right)}}{\csc^{2}{\left(2 a \right)}}}$$
/ 1 for 2*a mod pi = 0 | | 4 2 / 1 \ <4*cos (a)*tan (a)*|-1 + ---------| otherwise | | 2 | | \ tan (2*a)/ \
$$\begin{cases} 1 & \text{for}\: 2 a \bmod \pi = 0 \\4 \left(-1 + \frac{1}{\tan^{2}{\left(2 a \right)}}\right) \cos^{4}{\left(a \right)} \tan^{2}{\left(a \right)} & \text{otherwise} \end{cases}$$
/ 1 for 2*a mod pi = 0 | | / 2 \ < 2 | sin (4*a) | |sin (2*a)*|-1 + -----------| otherwise | | 4 | \ \ 4*sin (2*a)/
$$\begin{cases} 1 & \text{for}\: 2 a \bmod \pi = 0 \\\left(-1 + \frac{\sin^{2}{\left(4 a \right)}}{4 \sin^{4}{\left(2 a \right)}}\right) \sin^{2}{\left(2 a \right)} & \text{otherwise} \end{cases}$$
/ 1 for 2*a mod pi = 0 | | 2 | csc (2*a) |-1 + -------------- < 2/pi \ | csc |-- - 2*a| | \2 / |------------------- otherwise | 2 \ csc (2*a)
$$\begin{cases} 1 & \text{for}\: 2 a \bmod \pi = 0 \\\frac{\frac{\csc^{2}{\left(2 a \right)}}{\csc^{2}{\left(- 2 a + \frac{\pi}{2} \right)}} - 1}{\csc^{2}{\left(2 a \right)}} & \text{otherwise} \end{cases}$$
/ /pi \ | 0 for |-- + 4*a| mod pi = 0 | \2 / | | / pi\ < 2*cot|2*a + --| | \ 4 / |------------------ otherwise | 2/ pi\ |1 + cot |2*a + --| \ \ 4 /
$$\begin{cases} 0 & \text{for}\: \left(4 a + \frac{\pi}{2}\right) \bmod \pi = 0 \\\frac{2 \cot{\left(2 a + \frac{\pi}{4} \right)}}{\cot^{2}{\left(2 a + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}$$
/ 1 for 2*a mod pi = 0 | | 2/ pi\ | sec |2*a - --| | \ 2 / |-1 + -------------- < 2 | sec (2*a) |------------------- otherwise | 2/ pi\ | sec |2*a - --| | \ 2 / \
$$\begin{cases} 1 & \text{for}\: 2 a \bmod \pi = 0 \\\frac{-1 + \frac{\sec^{2}{\left(2 a - \frac{\pi}{2} \right)}}{\sec^{2}{\left(2 a \right)}}}{\sec^{2}{\left(2 a - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}$$
/ 1 for 2*a mod pi = 0 | | / 2 \ | | sin (4*a) | <(1 - cos(4*a))*|-1 + -----------| | | 4 | | \ 4*sin (2*a)/ |--------------------------------- otherwise \ 2
$$\begin{cases} 1 & \text{for}\: 2 a \bmod \pi = 0 \\\frac{\left(-1 + \frac{\sin^{2}{\left(4 a \right)}}{4 \sin^{4}{\left(2 a \right)}}\right) \left(- \cos{\left(4 a \right)} + 1\right)}{2} & \text{otherwise} \end{cases}$$
/ 1 for 2*a mod pi = 0 | | 2 / 1 \ |4*tan (a)*|-1 + ---------| | | 2 | < \ tan (2*a)/ |-------------------------- otherwise | 2 | / 2 \ | \1 + tan (a)/ \
$$\begin{cases} 1 & \text{for}\: 2 a \bmod \pi = 0 \\\frac{4 \left(-1 + \frac{1}{\tan^{2}{\left(2 a \right)}}\right) \tan^{2}{\left(a \right)}}{\left(\tan^{2}{\left(a \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}$$
/ 1 for 2*a mod pi = 0 | | / 2 \ | 2/ pi\ | cos (2*a) |
$$\begin{cases} 1 & \text{for}\: 2 a \bmod \pi = 0 \\\left(\frac{\cos^{2}{\left(2 a \right)}}{\cos^{2}{\left(2 a - \frac{\pi}{2} \right)}} - 1\right) \cos^{2}{\left(2 a - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}$$
/ 1 for 2*a mod pi = 0 | | 2 | sin (4*a) |-1 + ----------- | 4 < 4*sin (2*a) |---------------- otherwise | 2 | sin (4*a) |1 + ----------- | 4 \ 4*sin (2*a)
$$\begin{cases} 1 & \text{for}\: 2 a \bmod \pi = 0 \\\frac{-1 + \frac{\sin^{2}{\left(4 a \right)}}{4 \sin^{4}{\left(2 a \right)}}}{1 + \frac{\sin^{2}{\left(4 a \right)}}{4 \sin^{4}{\left(2 a \right)}}} & \text{otherwise} \end{cases}$$
// 1 for a mod pi = 0\
|| |
|| 2 |
/ 1 \ ||/ 2 \ |
|1 - ---------|*|<\-1 + cot (a)/ |
| 2 | ||--------------- otherwise |
\ cot (2*a)/ || 2 |
|| / 2 \ |
\\ \1 + cot (a)/ /
$$\left(1 - \frac{1}{\cot^{2}{\left(2 a \right)}}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod \pi = 0 \\\frac{\left(\cot^{2}{\left(a \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(a \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)$$
/ 1 for 2*a mod pi = 0 | | 2 | cos (2*a) |-1 + -------------- | 2/ pi\ | cos |2*a - --| < \ 2 / |------------------- otherwise | 2 | cos (2*a) | 1 + -------------- | 2/ pi\ | cos |2*a - --| \ \ 2 /
$$\begin{cases} 1 & \text{for}\: 2 a \bmod \pi = 0 \\\frac{\frac{\cos^{2}{\left(2 a \right)}}{\cos^{2}{\left(2 a - \frac{\pi}{2} \right)}} - 1}{\frac{\cos^{2}{\left(2 a \right)}}{\cos^{2}{\left(2 a - \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}$$
/ 1 for 2*a mod pi = 0 | | 2/ pi\ | sec |2*a - --| | \ 2 / |-1 + -------------- | 2 < sec (2*a) |------------------- otherwise | 2/ pi\ | sec |2*a - --| | \ 2 / | 1 + -------------- | 2 \ sec (2*a)
$$\begin{cases} 1 & \text{for}\: 2 a \bmod \pi = 0 \\\frac{-1 + \frac{\sec^{2}{\left(2 a - \frac{\pi}{2} \right)}}{\sec^{2}{\left(2 a \right)}}}{1 + \frac{\sec^{2}{\left(2 a - \frac{\pi}{2} \right)}}{\sec^{2}{\left(2 a \right)}}} & \text{otherwise} \end{cases}$$
/ 1 for 2*a mod pi = 0
|
| // 0 for 2*a mod pi = 0\
$$\begin{cases} 1 & \text{for}\: 2 a \bmod \pi = 0 \\\left(\cot^{2}{\left(2 a \right)} - 1\right) \left(\begin{cases} 0 & \text{for}\: 2 a \bmod \pi = 0 \\\frac{- \cos{\left(4 a \right)} + 1}{2} & \text{otherwise} \end{cases}\right) & \text{otherwise} \end{cases}$$
/ 1 for 2*a mod pi = 0 | | 2 | csc (2*a) |-1 + -------------- | 2/pi \ | csc |-- - 2*a| < \2 / |------------------- otherwise | 2 | csc (2*a) | 1 + -------------- | 2/pi \ | csc |-- - 2*a| \ \2 /
$$\begin{cases} 1 & \text{for}\: 2 a \bmod \pi = 0 \\\frac{\frac{\csc^{2}{\left(2 a \right)}}{\csc^{2}{\left(- 2 a + \frac{\pi}{2} \right)}} - 1}{\frac{\csc^{2}{\left(2 a \right)}}{\csc^{2}{\left(- 2 a + \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}$$
/ 1 for 2*a mod pi = 0
|
| // 0 for 2*a mod pi = 0\
| || |
| || 2 |
$$\begin{cases} 1 & \text{for}\: 2 a \bmod \pi = 0 \\\left(\cot^{2}{\left(2 a \right)} - 1\right) \left(\begin{cases} 0 & \text{for}\: 2 a \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(a \right)}}{\left(\cot^{2}{\left(a \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) & \text{otherwise} \end{cases}$$
Piecewise((1, Mod(2*a = pi, 0)), ((-1 + cot(2*a)^2)*Piecewise((0, Mod(2*a = pi, 0)), (4*cot(a)^2/(1 + cot(a)^2)^2, True)), True))